Issue 63

M. Khaise et alii, Frattura ed Integrità Strutturale, 63 (2023) 153-168; DOI: 10.3221/IGF-ESIS.63.14

        2 11 11 S

F f

≥ 1.0

(3)

If σ 11 ≥ 0 then the tensile matrix failure criteria is

2

2

  

  



   12

22

  

F m

≥ 1.0

(4)



F

 

 



m

S

S

22

12



If σ 11 < 0 then the compressive fiber failure criteria is

   

   

2

2

2

 S





s

22

22

22

12 12

  

  

  

  

  

  

  

  

F m









≥ 1.0

(5)

1

2 23 S

S

S

2 23

22

Concept of inflated pressure cavity has been considered to simulate the behavior of pipe with pressure changes and assure the application of uniform pressure. The pressure load was applied to the internal surface of the tube. The pressure load for all models started from internal pressure P i and gradually increased to the higher pressure. The interface between the steel pipe and repair laminate for model is assumed to be perfect bond using tie constraint.

R ESULTS AND DISCUSSIONS

N

umerical analysis is carried out for three cases: solid pipe without defect, pipe with defect and composite repair of wall loss defect pipe. Results of all three cases are discussed and compared with analytical failure pressure. In addition to that, an experimental failure pressure of composite repair of wall loss defect pipe is compared with the numerical modelling results. Lastly, an optimisation of composite repair thickness is carried out using numerical modelling. Pipe without defect Analytical failure pressure of pipe without defect is calculated based on the yield criterion and the analytical formula is given as:    2. . a f ext t S P D (6) ext D is the external diameter of pipe and a S is the allowable stress of pipe. The maximum sustained failure pressure of pipe can be determined from the above simple equation with considering the maximum yield strength of pipe as an allowable stress. The maximum failure pressure obtained    ( 386 ) a y S MPa from analytical formula is 32.61 MPa for the steel API-5L X56 pipe thickness of 7.11 mm and diameter of 168.3 mm (Tab. 2). The failure pressure obtained from numerical model is 34.6 MPa for the same configuration. It is clearly noticed (Tab. 4) that the numerical results are closely match with the analytical failure pressure with an acceptable error limit of 6%. The result of numerical analysis of von Mises stress of steel pipe without defect is shown in Fig. 6 and it shows that the pipe is experiencing a maximum 386 MPa stress for failure pressure of 34.6 MPa. Fig. 7 shows the true stress-strain and Ramberg Osgood stress-strain curve of API 5L X56 Steel. The design pressure of the pipe which is obviously the lower than the failure pressure and it can be calculated with the allowable limit by keeping the 28% margin:    0.72. . a d t S P r (7) where, t is the pipe thickness and

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